The Circle www.mathsrevision.com Isosceles Triangles in Circles Right angle in a Semi-Circle Tangent Line to a Circle Diameter Symmetry in a Circle Circumference of a Circle www.mathsrevision.com Length of an ARC of a Circle Area of a Circle Area of a SECTOR of a Circle Summary of Circle Chapter Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Starter Questions www.mathsrevision.com Q1. Calculate Area and perimeter 5cm 2cm 3cm 4cm Q2. 30% of 200 Q3. www.mathsrevision.com Q4. If a = 1 , b = 2 and c = 4 Find Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Isosceles triangles in Circles Aim of Today’s Lesson To identify isosceles triangles within a circle. www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Isosceles triangles in Circles When two radii are drawn to the ends of a chord, An isosceles triangle is formed. A B www.mathsrevision.com C Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Isosceles triangles in Circles Special Properties of Isosceles Triangles Two equal lengths www.mathsrevision.com Two equal angles Angles in any triangle sum to 180o Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Isosceles triangles in Circles Q. Find the angle xo. Solution Angle at C is equal to: B www.mathsrevision.com xo C Since the triangle is isosceles we have A 280o Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Isosceles triangles in Circles Begin Maths in Action Book page 181 www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Starter Questions www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Semi-circle angle Aim of Today’s Lesson To find the angle in a semi-circle made by a triangle with hypotenuse equal to the diameter and the two smaller lengths meeting at the circumference. www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Semi-circle angle www.mathsrevision.com Tool-kit required 1. Protractor www.mathsrevision.com 2. Pencil 3. Ruler Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Semi-circle angle www.mathsrevision.com 1. Using your pencil trace round the protractor so that you have semi-circle. 2. Mark the centre of the semi-circle. www.mathsrevision.com You should have something like this. Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Semi-circle angle x x x www.mathsrevision.com x x x x x x Mark three points Outside the circle x x x 2. On the circumference x x 3. Inside the circle www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Semi-circle angle Log your results in a table. www.mathsrevision.com x For each of the points Form a triangle by drawing a line from each end of the diameter to the point. Measure the angle at the various points. x x www.mathsrevision.com Log your results in a table. Inside Circumference Outside Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Begin Maths in Action Book page 182 Semi-circle angle x x x Inside Circumference Outside < 90o = 90o > 90o www.mathsrevision.com Begin Maths in Action Book page 182 Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Write down as many equations as you can Starter Questions If a = 7 b = 4 and c = 10 Write down as many equations as you can www.mathsrevision.com e.g. a + b = 11 Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Tangent line Aim of Today’s Lesson To understand what a tangent line is and its special property with the radius at the point of contact. www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Tangent line www.mathsrevision.com A tangent line is a line that touches a circle at only one point. Which of the lines are tangent to the circle? www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Tangent line www.mathsrevision.com The radius of the circle that touches the tangent line is called the point of contact radius. Special Property The point of contact radius is always perpendicular (right-angled) to the tangent line. www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Tangent line www.mathsrevision.com Q. Find the length of the tangent line between A and B. Solution Right-angled at A since AC is the radius at the point of contact with the Tangent. B 10 www.mathsrevision.com By Pythagoras Theorem we have A C 8 Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Begin Maths in Action Book page 185 Tangent line Begin Maths in Action Book page 185 www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Starter Questions www.mathsrevision.com Q1. Calculate Area and perimeter 10cm 3cm 5cm 7cm Q2. 15% of 280 Q3. www.mathsrevision.com Q4. If x = -1 , y = 3 and z = 10 Find Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Diameter symmetry Aim of Today’s Lesson To understand some special properties when a diameter bisects a chord. www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Diameter symmetry C D O A B A line drawn through the centre of a circle through the midpoint a chord will ALWAYS cut the chord at right-angles O A line drawn through the centre of a circle at right-angles to a chord will ALWAYS bisect that chord. A B A line bisecting a chord at right angles will ALWAYS pass through the centre of a circle. Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Diameter symmetry www.mathsrevision.com Q. Find the length of the chord A and B. Solution Radius of the circle is 4 + 6 = 10. B Since yellow line bisect AB and passes through centre O, triangle is right-angle. 10 O www.mathsrevision.com By Pythagoras Theorem we have 4 6 Since AB is bisected The length of AB is A Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Begin Maths in Action Book page 187 Diameter symmetry Begin Maths in Action Book page 187 www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Starter Questions www.mathsrevision.com Q1. Q2. 12 8 Q3. Calculate the area of the triangle www.mathsrevision.com Q4. Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Circumference of a circle Aim of Today’s Lesson To be able to use the formula for calculating the circumference of a circle www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Circumference of a circle Main parts of the circle radius O www.mathsrevision.com Diameter Circumference Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Circumference of a circle Q. Find the circumference of the circle ? Solution 4cm www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Circumference of a circle The circumference of the circle is 60cm ? Find the length of the diameter and radius. Solution www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Circumference of a circle Now it’s your turn ! Begin Maths in Action Book page 190 www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Starter Questions www.mathsrevision.com Q1. Calculate Q2. Make D the subject of the equation. www.mathsrevision.com Q3. Q4. Calculate Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

length of the arc of a circle Aim of Today’s Lesson To find and be able to use the formula for calculating the length of an arc. www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

length of the arc of a circle Q. What is an arc ? Answer An arc is a fraction of the circumference. A www.mathsrevision.com minor arc major arc B Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

length of the arc of a circle Q. Find the circumference of the circle ? Solution 10cm www.mathsrevision.com Maths in Action Book Exercise 1 Questions 1 & 2 Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

length of the arc of a circle Q. Find the arc length for the semi-circle ? Solution www.mathsrevision.com 180o Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

length of the arc of a circle Q. Given part of the circle below. Find the arc length ? Solution 10cm 90o www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

length of the arc of a circle 3 step process to calculating the length of an arc. Step 1 Find the circumference of the circle. Step 2 Find fraction of the whole circle. www.mathsrevision.com Step 3 Find the arc length. Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

length of the arc of a circle Q. Part of a circle is given below. Find the arc length. Fraction of circle 6cm 45o Solution www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

length of the arc of a circle 3 step process to calculating the length of an arc. Step 1 Find the circumference of the circle. Step 2 Find fraction of the whole circle. www.mathsrevision.com Step 3 Find the arc length. Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

length of the arc of a circle Q. Find the length of the arc AB below ? Solution A 9 cm www.mathsrevision.com 60o B Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

length of the arc of a circle Now it’s your turn ! Begin Maths in Action Book page 193 www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Starter Questions www.mathsrevision.com Q1. Find all missing angles Q2. List the prime numbers between 10 and 20. www.mathsrevision.com Q3. Solve 4cm Q4. Calculate the area of the shape. 5cm Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty 10cm

The Area of a circle Aim of Today’s Lesson To come up with and be able to use the formula for calculating the area of a circle www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

And lay them out side by side The Area of a circle If we break the circle into equal sectors And lay them out side by side We get very close to a rectangle. 1 2 3 4 5 6 7 8 www.mathsrevision.com 5 6 7 8 2 4 3 1 Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

The Area of a circle www.mathsrevision.com 8 2 4 6 3 1 5 7 If we cut the sectors Thinner and thinner then we get closer and closer to a rectangle. Hence we can represent the area of a circle by a rectangle. 1 2 3 4 5 6 7 8 thinner and thinner sectors www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

The Area of a circle www.mathsrevision.com But the area inside this rectangle is also the area of the circle Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

The Area of a circle www.mathsrevision.com Q. Find the area of the circle ? Solution 4cm www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Begin Maths in Action Book The Area of a circle Now it’s your turn ! Begin Maths in Action Book Ex9.1 page 194 Q1-2 www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

The Area of a circle www.mathsrevision.com Find area of the circle? The diameter of the circle is 60cm. Find area of the circle? Solution www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Begin Maths in Action Book The Area of a circle Now it’s your turn ! Begin Maths in Action Book Ex9.1 page 194 Q3-4 www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

The Area of a circle www.mathsrevision.com Find its radius? The area of a circle is 12.64 cm2. Find its radius? Solution www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Begin Maths in Action Book The Area of a circle Now it’s your turn ! Begin Maths in Action Book Ex9.1 page 194 Q5 onwards www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Starter Questions www.mathsrevision.com Q1. Factorise Q2. Make h the subject of the equation. Q3. Calculate www.mathsrevision.com Q4. The value of the standard deviation for petrol prices in Glasgow is 2.1 and 1.9 for Edinburgh. Comparing the two values write down a valid statement. Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Sector area of a circle Aim of Today’s Lesson To find and be able to use the formula for calculating the sector of an circle. www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Sector area is a fraction Sector area of a circle Q. What is an sector area ? Answer Sector area is a fraction of the area of the whole circle. A www.mathsrevision.com minor sector major sector B Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Sector area of a circle www.mathsrevision.com Q. Find the area of the circle ? Solution 10cm www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Sector area of a circle www.mathsrevision.com Q. Find the sector area for the semi-circle ? Solution 10cm www.mathsrevision.com 180o Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Sector area of a circle www.mathsrevision.com Q. Given part of the circle below. Find the sector area ? Solution www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Sector area of a circle www.mathsrevision.com 3 step process to calculating sector area of a circle. Step 1 Find the area of the circle. Step 2 Find fraction of the whole circle. www.mathsrevision.com Step 3 Find the sector area. Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Sector area of a circle www.mathsrevision.com Q. Part of a circle is given below. Find the sector area. Fraction of circle 6cm 45o Solution www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Sector area of a circle www.mathsrevision.com 3 step process for calculating the sector area. Step 1 Find the area of the circle. Step 2 Find fraction of the whole circle. www.mathsrevision.com Step 3 Find the sector area. Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Sector area of a circle www.mathsrevision.com Q. Find the area of the sector below ? Solution www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Begin Maths in Action Book page 196 Sector area of a circle Now it’s your turn ! Begin Maths in Action Book page 196 www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Starter Questions www.mathsrevision.com 115o Q1. Find all the missing angles Q2. Calculate www.mathsrevision.com Q3. The cost of a new computer is £1000 +vat. If the vat is charged at 12% what is the total cost. Q4. The cost of a bag of sugar is £1.12. How much 50 bags cost. Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Summary of Circle Topic Arc length is Pythagoras Theorem SOHCAHTOA line that bisects a chord Splits the chord into 2 equal halves. Makes right-angle with the chord. Passes through centre of the circle Circumference is Semi-circle angle is always 90o Area is www.mathsrevision.com Tangent touches circle at one point and make angle 90o with point of contact radius Radius Diameter Sector area Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty

Summary of Circle Topic Maths in Action Book Page 199 www.mathsrevision.com Saturday, 22 September 2018Saturday, 22 September 2018 Created by Mr Lafferty